A tank contains `100` kg of salt and `2000` L of water. A solution of a concentration `0.025` kg of salt per liter enters a tank at the rate `6` L/min. The solution is mixed and drains from the tank at the same rate.
Find the equation for the amount of salt in the tank after t hours.
The Attempt at a Solution
I have 0.15kg/min as my rate in and y(t)/333.33 as my rate out.
Which I put together in the form
dy/dt = (5 - y(t))/(333.33)
Split it into
int of (dy/5 - y) = int of (dt/333.33)
-ln(5 - y) = t/333.33 + C
y(0) = 100, so C = -ln(-95)
-ln(5 - y) = t/(333.33) - ln(-95)
5 - y = -95e^(-t/333.33)
y(t) = 5 + 95e^(-t/333.33)
But that's wrong. I know I've asked alot of stuff today, but this one is driving me crazy, I've tried everything I could think of and nothing came out right. Help!